这样断句：we are taking a little detour from the grand styles of public architecture(that) we've been studying,to look at residential architecture in the US.
就是说：今天,我们稍微绕开我们正在学习的公共建筑的宏伟风格,来看一看美国的居民建筑.
我标了that的地方后面做定语从句修饰architecture,to后面是个目的状语从句.